Anomalous vortex melting line in the two-component superconductor $(\mathrm{Cu},\mathrm{C}){\mathrm{Ba}}_2{\mathrm{Ca}}_3{\mathrm{Cu}}_4{\mathrm{O}}_{10+\delta }$

Using the on-set of third-harmonic susceptibility we have measured vortex melting lines of high-pressure synthesized $\left({\mathrm{Cu}}_{0.6}{\mathrm{C}}_{0.4}\right){\mathrm{Ba}}_2{\mathrm{Ca}}_3{\mathrm{Cu}}_4{\mathrm{O}}_y$ [(Cu,C):1234] and $\left({\mathrm{Cu}}_{0.5}{\mathrm{C}}_{0.5}\right){\mathrm{Ba}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ [(Cu,C):1223] with preferentially oriented crystallites and having various carrier concentrations. Vortex melting lines of all (Cu,C):1223 samples and of optimum-doped (Cu,C):1234 were very well described by the commonly accepted theory of melting lines within the two-fluid model. Overdoped (Cu,C):1234 proved to have an anomalous melting line, that was phenomenologically explained by the rather special gaps evolution, that is the significant opening of a second superconducting gap due to $\mathrm{Cu}{\mathrm{O}}_2$ outer planes at a temperature lower than the critical one, where the first superconducting gap due to inner planes opens. The experimental melting lines of overdoped (Cu,C):1234 were modelled theoretically by assuming an empirical formula for the temperature dependence of anisotropy factor.

Figure 1

X-ray diffraction pattern of over-doped (Cu,C):1234. The stars indicate a very small amount of infinite-layer compound $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2$.

Figure 2

(Color online) Temperature dependence of out-of-phase and third-harmonic susceptibility of overdoped (Cu,C):1234, in dc field of $5\mathrm{kOe}$, ac field amplitude of $50\mathrm{mOe}$, and ac field frequency of $10\mathrm{kHz}$.

Figure 3

(Color online) Experimentally determined vortex melting lines of (Cu,C):1223 (optimum doped, full circles; slightly overdoped, open circles; and overdoped, open squares), and of (Cu,C):1234 (optimum doped, triangles; overdoped, full squares). Full lines represent one-parameter fits with Eq. (1) using two-fluid model for the temperature dependence of the in-plane penetration depth.

Figure 4

(Color online) Experimentally determined vortex melting line of over-doped (Cu,C):1234 (full squares). Dot and full lines represent fits described in the text. Inset shows the proposed empirical temperature dependence of anisotropy factor, Eq. (2), with the parameters resulting from fits.